# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{\left(5^2-7^x\right)}{cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

Learn how to solve trigonometric equations problems step by step online.

$\frac{25-7^x}{\cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation (5^2-7^x)/(cos((3.141592653589793/8))=9/5. Calculate the power 5^2. Calculating the cosine of \frac{\pi}{8} degrees. Multiply both sides of the equation by 0.9239. We need to isolate the dependent variable x, we can do that by subtracting 25 from both sides of the equation.

$x=1.6188$

### Problem Analysis

$\frac{\left(5^2-7^x\right)}{cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

### Main topic:

Trigonometric Equations

~ 0.05 seconds